In right triangle ABC shown below, the midpoint of hypotenuse AC is located at D and segment BD is drawn. AB = 12 and BC =16, then explain why BD=10. Hint: consider what you know about the diagonals of a
rectangle.

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  diagonal AC is 20, so all half-diagonals are 10. BD is one such.

Step-by-step explanation:

The length of hypotenuse AC is given by the Pythagorean theorem:

  AC² = AB² + BC²

  AC² = 12² +16² = 400

  AC = √400 = 20

The midpoint of AC is 10 units from A and from C.

Consider point E that finishes rectangle ABCE. Then diagonals BE and AC meet at their midpoints, D. The diagonals of a rectangle are the same length, so the four half-diagonals are congruent:

  AD = CD = ED = BD = 10

Alternate solution

The "rise" from BC to D is half of AB, so is 6.

The "run" from AB to D is half of BC, so is 8.

The Pythagorean theorem tells you BD = √(6² +8²) = 10.

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